Single nucleotide polymorphism (SNP) data can be used for parameter estimation via maximum likelihood methods as long as the way in which the SNPs were determined is known, so that an appropriate likelihood formula can be constructed. We present such likelihoods for several sampling methods. As a test of these approaches, we consider use of SNPs to estimate the parameter Theta = 4N(e)micro (the...

We obtain infinite product expansions in the sense of Borcherds for theta functions associated with certain positive-definite binary quadratic and hermitian forms. Among other things, we show that every weight 1 function is a product. In particular, have zeros only at irrationals.

Lucy Slater used Bailey’s 6ψ6 summation formula to derive the Bailey pairs she used to construct her famous list of 130 identities of the Rogers-Ramanujan type. In the present paper we apply the same techniques to Chu’s 10ψ10 generalization of Bailey’s formula to produce quite general Bailey pairs. Slater’s Bailey pairs are then recovered as special limiting cases of these more general pairs. I...

It is well known that the unitary evolution of a closed $M-$level quantum system can be generated by non-Hermitian Hamiltonian $H$ with real spectrum. Its Hermiticity restored via an amended inner-product metric $\Theta$. In Hermitian cases evaluation spectrum (i.e., bound-state energies) usually achieved diagonalization Hamiltonian. (or, more precisely, in $\Theta-$quasi-Hermitian) mechanics w...

LAU-0901, a novel platelet-activating factor (PAF) receptor antagonist, is highly neuroprotective in a rodent model of cerebral ischemia. This study was conducted to establish whether the neuroprotection induced by LAU-0901 persists with chronic survival. Male Sprague-Dawley rats were anesthetized with isoflurane and subjected to 2 h of temporary middle cerebral artery occlusion (MCAo) induced ...

In Ramanujan’s final letter to Hardy, he wrote of a strange new class of infinite series he called “mock theta functions”. It turns out all of Ramanujan’s mock theta functions are essentially specializations of a so-called universal mock theta function g3(z, q) of Gordon–McIntosh. Here we show that g3 arises naturally from the reciprocal of the classical Jacobi triple product—and is intimately ...

The Riemann-Wirtinger integral is a function defined by a definite integral on a complex torus whose integrand is a power product of the exponential function and theta functions. It was found as a special solution of the system of differential equations which governs the monodromy-preserving deformation of Fuchsian differential equations on the complex torus [11], [12]. The main purpose of this...